research article shock analysis on a packaged washing...

Research ArticleShock Analysis on a Packaged Washing Machine from DamageBoundary Shock Response Spectrum to Component Failure

Jing Qian12 Heping Cai12 Weiwei Ma1 and Zhiwei Hao1

1Packaging Engineering Department Jiangnan University Wuxi Jiangsu 214122 China2Key Laboratory of Advanced Manufacturing Equipment Technology Jiangsu 214122 China

Correspondence should be addressed to Jing Qian qj639163com

Received 29 July 2014 Revised 25 November 2014 Accepted 26 November 2014

Academic Editor Ahmet S Yigit

Copyright copy 2015 Jing Qian et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Both analyses of the damage boundary and shock response spectrum (RSR) are the basis for the development of the protectivepackaging systemThe shock analysis through lab test and numerical simulation found that the root cause of packaging failure wasdue to the stress of the critical component beyond the yield limit of the material Lab shock test data showed that the packagingdesign based on the damage boundary is conservative and the RSR could be helpful and provide support to develop more effectivepackaging system Furthermore numerical simulation can accurately analyze the component and the entire product packagingsystem in great detail

1 Introduction

Shock is a transient physical excitation and a mechanicalshock is a sudden change in velocity and acceleration of anobject caused for example by impact drop and kick It isusually measured by an accelerometer and described as ashock pulsemdasha plot of acceleration change versus time Oneof the packaging goals is to protect the product from damagecaused by the mechanical shock

In the 1970s Dr Newton [1] of Monterey ResearchLaboratory developed and validated the damage boundaryconcept at Michigan State University Few years later incor-porated by the American Society for Testing and Materials(ASTM) into D3332 [2] the packaging industry was affordeda practical tool for determining the fragility of commercialproducts

The damage boundary is normally expressed as a plot ofpeak acceleration versus velocity change as shown in Figure 1[3]The vertical line critical velocity change (Δ119881

119888) represents

the velocity change which can be related to the drop heightbelow which no product damage will occur regardless of thepeak acceleration The horizontal line critical acceleration(119860119888) represents the acceleration and above at which the

product will be damaged if velocity significantly exceedsΔ119881119888

Half-sine pulses are used to find the critical velocitychange line (at which point the product breaks and must berepaired or replaced) and square wave pulses are used tofind the critical acceleration line (breaking another product)The damage boundary theory followingD3332 has now beenon the books for more than 40 years It is widely acceptedand this approach is taught and practiced in various formsworldwide

From a practical standpoint along with extensive useof the damage boundary came the realization that packagedesigns based solely on critical acceleration are sometimesquite conservativeThewave shape which will be transmittedby the cushion is essentially never a square wave andthe damage boundary only considers the input shock pulsethus the whole packaging system is ignored Therefore animproved approach to relate product fragility and packageperformance is obviously needed

The use of shock response spectrum (SRS) analysismay provide such an approach SRS analysis calculates theresponses of a large number of theoretical single degree offreedom spring-mass systems to a given shock pulse An SRSplot is a graph of the absolute value of the peak responseaccelerations of each spring-mass system plotted at theirvarious natural frequencies [4] For the input from pulse

Hindawi Publishing CorporationShock and VibrationVolume 2015 Article ID 462492 7 pageshttpdxdoiorg1011552015462492

2 Shock and Vibration

Peak

acce

lera

tion

No damage

No

dam

age

Damage

Ac

ΔVc Velocity change

Figure 1 The damage boundary

shock (shock table) that causes damage to the product anSRS is calculatedThis calculated shock response spectrum iscalled 119878

119888 the ldquocriticalrdquo SRSThen 119878

119888 rather than119860

119888 becomes

the design target for protective packaging When droppingfrom predetermined height the SRS of the response shockpulse transmitted by the cushioning to product needs to liebelow 119878

119888

From then on many researchers worked on the theo-retical analysis of the shock response of different linear ornonlinear cushioning packaging systems with various shockpulses [5ndash10] and the conducting study was graduated indepth fromone-degree to three-degree systems [11ndash13] Shockresponse spectrum is now wildly used in experimental testsconsidering not only shock condition but also vibration [1415]

Inmany cases damage of products happened along struc-tural elements and damage of structural elements caused thefailure of products Suhir theoretically analyzed the shock andvibration responses of circuit boards of portable electronicproducts and found that the maximum dynamic stress isthe key factor which caused the failure of the product [16]The research on the packaging system of impeller washingmachine gave a similar conclusion

2 The Packaging System ofthe Washing Machine

An impeller washing machine is composed of a washingtank a suspension system and an outer tankThe suspensionsystem is made up of four suspenders which suspend thewashing tank inside the outer tank which decreases trans-mitted vibrations from working washing tank During thedelivery the washing machine is packed with a top cushionpad a bottom cushion pad and four corner holders (seeFigure 2) At the center of the bottom cushion pad there is araised bulge which can uplift the washing tank to release thesuspension

The cushion packaging (the cushion material thick ofcrash pad and so on) of washingmachinewas designed basedon damaged boundary Figure 3 shows the designed cushionmats

In this research the cushion material was polystyrenefoam The subsequent statistic data show that 20 damages

1998400

1

2

3

2998400

3998400

Figure 2 Cushion packaging of an impeller washing machine 1outer tank 2 suspender 3 washing tank 11015840 top cushion pad 21015840corner holder 31015840 bottom cushion pad

came from a suspension system whose suspenders werestraightenedThe result confused engineers Considering thatthe damage boundary does not include the whole cushionpackage the researcher decided to find out not only thefragility of the washing machine but also the shock responseof the packing system

3 Shock Tests on Unpackaged andPackaged Washing Machine

Test equipment MTS886241 shock test system LansmontTest Partner 3 (TP3) data acquisitions system andDASP dataacquisition system

The shock tests followed ASTM D3332-99 and theschematic diagram of the shock test is shown in Figure 4 [17]During the test the packaging case system of the washingmachine was fastened to the shock table Because the mainprotection is the bottom cushion pad the other cushion padswere ignored in the test Two accelerometers were used onefastened to the shock table and the other at the bottom centerof washing tank to record the input shock pulse and theresponse of washing machine respectively The two differentdata acquisition systems have their own accelerometers andthey were in pairs fixed very close to make sure each pairinggets almost the same signal

To confirm that the two data acquisition systems couldgive same recordings a field test was set up and the acquiredsignals from two channels were shown in Figure 5 In thetests half-sine shock pulse was provided by a wave generatorprovided

As shown in Figure 5 the maximum acquired accelera-tions were 908023ms2 (from DASP) and 90287ms2 (fromTP3) respectivelyThedifference of two systems is 06 Bothintervals of two peak accelerations from two different systemsare 01 sTherefore the records from the two systems aremuchclose to each other

Shock and Vibration 3

(a) (b)

(c)

Figure 3 Cushion mats on the washing machine (a) Top cushion pad (b) bottom cushion pad (c) corner holder

Fence

Outer tank

Suspender

Washing tankBottom crash pad

Shock table

Drop height

Wave generator

Acceleration sensor

Input 1

Input 2Signal collection andanalysis system

(a) Schematic diagram (b) Test photo

Figure 4 Shock test on washing machine packaging system


000 002 004 006 008 010 012

05

04

03

02

01

00

minus01

minus02

minus03

minus04

minus05

times104

Time (s)

Acce

lera

tion

(ms

2 )

(a) DASP

1000

Acce

lera

tion

(ms

2 )

0

Time (ms)

120010008006004002000

minus200minus400minus600minus800minus1000minus1200

(b) TP3

Figure 5 Acquired signal on the 50mm drop height

(a) Normal (b) Straightened

Figure 6 Suspender

31 Shock Tests on Unpacked Washing Machine In thissection the washing machine was fastened directly to theshock table without any cushion padsThe half-sine pulse wasset up as an input shock pulse to the shock table Shock testsstarted from 50mm drop height Increasing the drop heightone of the suspenders was straightened as shown in Figure 6when the drop height reached 150mm The shock test at the150mm drop height was repeated twice the test found thattwo suspenders were straightened each time

Table 1 gives the maximum accelerations acquired fromdifferent channels at various drop heights Normally theaccelerations were recorded as multiples of the gravitationalacceleration (G)

The fragility of the washing machine is normally between90G and 120G as cited in MIL-HDBK-304 [18] FromTable 1 it is clear that the product is still safe even whenthe acceleration of the input pulse reached 1523 G Thesuspenders failed only when the input acceleration reached1716 G Thus the package design as based solely on thedamage boundary is quite conservative

32 The Shock Test on the Packed Washing Machine A half-sine pulse was provided as an input shock pulse to washingmachine with the bottom cushion pad fastened to the shock

Table 1 Maximum accelerations acquired from different channelson the unpacked product

Drop height(mm)

Input accelerations (G)(shock table)

Response accelerations (G)(center of washing tank)

50 908 24070 1143 292100 1382 500120 1523 1274150 (failure) 1716 1501

table Shock tests began at a 150mm drop height The dropheight was increased until 400mm when one straightenedsuspender failed The shock tests were repeated twice at a400mm drop height Two suspenders were straightened andthe bottom cushion pad was damaged (see Figure 7) eachtime

Table 2 shows the maximum accelerations acquired fromdifferent channels at various drop heights Multiples of thegravitational acceleration were used to express the maximumacceleration

As shown in Table 2 the packaged washing machinewas intact even when the input acceleration reached 2213 G


Figure 7 The broken bottom cushion pad after the shock test at a400mm drop height

Acce

lera

tion

(ms

2 )

Time (s)

500

400

300

200

100

0

minus100

minus200

minus300

minus400

minus500000 002 004 006 008 010 012

Figure 8 The response acceleration curve at a 400mm drop heightvia DASP

Table 2 The maximum accelerations acquired from differentchannels on packed product

Drop height(mm)



150 1752 253250 1904 295350 2213 369400 (failure) 2441 448

Figure 8 shows the response acceleration curve at a 400mmdrop height of the packaged washing machine

The acquired data were processed using the SRS analysisvia the ETC module of TP3 The positive SRS curve ofthe packaged washing machine was achieved as shown inFigure 9 It clearly shows that the maximum acceleration ofwashing machine packaging system is 11432ms2 when thefrequency is 83542Hz The SRS curve could be the ldquocriticalrdquoSRS of this packaging system Each point on the SRS curverepresents the critical acceleration 119878

119888for the corresponding

frequency In other words when the packaging system isdelivered and the response acceleration is below the critical

0

20

40

60

80

100

120

140

0 5000 10000 15000 20000 25000

Acce

lera

tion

(ms

2 )

Fn (Hz)

Figure 9 The positive SRS curve

acceleration 119878119888at every corresponding frequency then the

washing machine is safe

4 Numerical Computation on Key StructuralElements of the Washing Machine

Each product has its weakest element which is the easiestto be damaged during transport The weakest element inthe packaging system is called the critical element Basedon the statistical data and the aforementioned research thecritical element of the washing machine is its suspendersActually the damage of suspenders is plastic deformationand this damage essentially happened because the stress of thecritical element is beyond the allowable stress (yield strength)of the material In this case the numerical computation viaANSYSLS-DYNA finite element software was used to seewhat happened as the drop height approached 400mm

41 The Development of the Computer Model on the Pack-aging System The computer model of the washing machinepackaging system [19] is composed of the washing tank theouter tank four suspenders and cushion pads as shown inFigure 10The properties of the materials are listed in Table 3

Following Chinese national standard GBT 8168-2008[20] the compression test on the cushion material (EPS)was performed on the LRX Plus Universal Material TestingMachine The stress-strain curve is shown in Figure 11

To verify the viability of the developed model the shockon the unpackaged washing machine was simulated byANSYS software Figure 12 shows the plot of accelerationversus time when the shock happened at a 50mm dropheight Node A is on the bottom-center of the washing tank(the location of accelerometer for the shock test as shownin Figure 4) and node B is on the middle of washing tankThe acceleration-time history of node A agreed well with thatobtained by shock table apparatus

The maximum acceleration of node A is 238ms2 Bycomparing with shock test data in Table 1 the responseacceleration is 24G (2352ms2) when the drop height is50mm The error of simulation is 12 and the developedmodel has sufficient accuracy By comparing with node Aand node B it is clear that the peak acceleration of node B issmaller and lags slightly behind nodeA as shown in Figure 12


Table 3 Properties of materials

Part name Material Elastic modulus (GPa) Density (Kgm3) Poissonrsquos ratioSuspender Q345 210 7850 03Outer tank 08F 205 7850 03Washing tank PP 106 910 040ndash043Spring 65Mn Cushion pad EPS 08 20 01Ground Rigidity 210 7850 02

Washing tank Outer tank Suspender Crash pad Packaging case model

+ + +x

yz

xy

z

y

z

Figure 10 The computer model of the washing machine packaging system

Strain ()

Stre

ss (M

Pa)

05

04

03

02

01

00

0 10 20 30 40 50 60 70 80

Figure 11 The stress-strain curve of the cushion material

Using the developed model of the packaged washingmachine the results of the simulation focus on the stresscondition of the suspender Figure 13 shows the change ofaxial force on suspender node 12055 which is proximal to theouter tankwhen the drop height is 350mmNode 12055 is thepoint where the maximum axial force happened

When the drop height is 350mm the maximum axialforce of the suspender is 154 kN The cross sectional area is50mm2 so the axial stress is 308MPa Actually the suspenderis a real pull rod so the axial stress of suspender is a vonMises stress The yield limit of Q345 (material of suspender)is 345MPa The computation result is very close to the yieldlimit of the suspender Table 4 shows the maximum axial

AA

AA

A

B

BB B B

25

20

15

10

5

0

minus5

minus10

LS-DYNA user input

0 1 2 3 4 5

Time (E minus 03) (s)Node number

B4379A4632

Z-a

ccel

erat

ion

(E+3

) (m

ms

2 )

Figure 12 The acceleration response of the washing tank ondifferent nodes for a 50mm drop height

stress of the suspender when the equivalent drop height isclose to 350mm

Table 3 shows that when the drop height reaches 360mmthe axial stress of the suspender is beyond the yield limit of thematerial and plastic deformation will happen for examplethe suspender will be straightenedThe computational resultsmatch the results of the shock tests on the washing machinepackaging system

5 Conclusion

The research discussed shock tests and computer simulationto figure out the real reason that leads to damage of the criticalelement of the impeller washing machine packaging system


A

AA

A A

Element number12055

10

5

0

minus5

minus10

minus15

minus200 1 2 3 4 5

Time (E minus 03) (s)

Axi

al fo

rce (

E+3

) (N

)

A

LS-DYNA user input

Figure 13 The axial force of suspender node 12055

Table 4 The axial stresses of the suspender with different dropheights

Equivalent drop height (mm) The maximum axial stress of thesuspender (MPa)

360 355350 308340 290

The stress of the critical component beyond the yield limitof the material is the root cause Packaging design based onthe damage boundary of the product is quit conservative andthe shock response spectrum could be more reliably usedfor packaging evaluation and designmdashthe SRS of responseacceleration transmitted by cushioning to the product mustbe below the critical acceleration 119878

119888at every corresponding

frequency Hence numerical simulation can be used as areliable tool and providemore detailed analysis of the productpackaging system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the FundamentalResearch Funds for the Central Universities and Six TalentPeaks Funding from Jiangsu Province

References

[1] R E Newton Fragility Assessment Theory and Test ProcedureMonterey Research Laboratory Monterey Calif USA 1968

[2] American Society for Testing and Materials ldquoASTMD3332standard test methods for mechanical shock fragility of prod-ucts using shock machinesrdquo in Annual Book of ASTM Stan-dards vol 1509 2010

[3] W I Kipp ldquoDevelopments in testing products for distributionrdquoPackaging Technology and Science vol 13 no 3 pp 89ndash98 2000

[4] W I Kipp ldquoPSD and SRS in simple termsrdquo in Proceedings ofthe International Safe Transit Association Conference (ISTA rsquo98)Orlando Fla USA 1998

[5] Z Wang D Wu and J Qian ldquoThe shock response of tangentialnonlinear packaging system under the action of rectangularpulserdquo Journal of Vibration and Shock vol 18 no 3 pp 48ndash521999

[6] Z Wang and G Xiaoting ldquoThe shock characteristics of hyper-bolic tangent packaging system under the action of half-sinepulserdquo Packaging Engineering vol 2 no 20 pp 4ndash7 1999

[7] X Gong and Z Wang ldquoThe shock characteristics of hyperbolictangent packaging system under the action of rectangularpulserdquo Packaging Engineering vol 20 no 3 pp 12ndash15 1999

[8] J Wang F Duan J-H Jiang L-X Lu and Z-WWang ldquoDrop-ping damage evaluation for a hyperbolic tangent cushioningsystem with a critical componentrdquo Journal of Vibration andControl vol 18 no 10 pp 1417ndash1421 2012

[9] J Wang Y Khan R-H Yang L-X Lu and Z-W WangldquoDynamical behaviors of a coupled cushioning packagingmodel with linear and nonlinear stiffnessrdquo Arabian Journal forScience and Engineering vol 38 no 6 pp 1625ndash1629 2013

[10] A-J Chen ldquoThe shock characteristics of tilted support springpackaging system with critical componentsrdquo Shock and Vibra-tion vol 2014 Article ID 496035 8 pages 2014

[11] E Suhir ldquoDynamic response of a one-degree-of-freedom linearsystem to a shock load during drop tests effect of viscousdampingrdquo IEEE Transactions on Components Packaging andManufacturing Technology Part A vol 19 no 3 pp 435ndash4401996

[12] V P Sergey ldquoOptimal protection of two-degree-of-freedomsystem from shock and vibrationrdquo in Proceedingsof International Conference Physics and Control vol 4 pp1206ndash1208 IEEE Saint Petersburg Russia 2003

[13] J Wang Z-W Wang L-X Lu Y Zhu and Y-G WangldquoThree-dimensional shock spectrum of critical component fornonlinear packaging systemrdquo Shock and Vibration vol 18 no 3pp 437ndash445 2011

[14] T S Edwards ldquoPower delivered to mechanical systems byrandom vibrationsrdquo Shock and Vibration vol 16 no 3 pp 261ndash271 2009

[15] S Goyal J M Papadopoulos and P A Sullivan ldquoShockprotection of portable electronic products shock responsespectrum damage boundary approach and beyondrdquo Shock andVibration vol 4 no 3 pp 169ndash191 1997

[16] E Suhir ldquoIs the maximum acceleration an adequate criterion ofthe dynamic strength of a structural element in an electronicproductrdquo IEEE Transactions on Components Packaging andManufacturing Technology Part A vol 20 no 4 pp 513ndash5171997

[17] WMaThecushion packaging ofwashingmachine based on shockresponse spectrum [MS thesis] Jiangnan University 2008

[18] MIL-HDBK-304 Department of Defense Handbook PackageCushioning Design 1997

[19] Z Hao Dropping simulation analysis on key element of impellerwashing machine [MS thesis] Jiangnan University 2009

[20] GBT 8168-2008 TestingMethod of Static Compression for Pack-aging Cushioning Materials China National Standard 2008

International Journal of

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RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Peak

acce

lera

tion

No damage

No

dam

age

Damage

Ac

ΔVc Velocity change

Figure 1 The damage boundary

shock (shock table) that causes damage to the product anSRS is calculatedThis calculated shock response spectrum iscalled 119878

119888 the ldquocriticalrdquo SRSThen 119878

119888 rather than119860

119888 becomes

the design target for protective packaging When droppingfrom predetermined height the SRS of the response shockpulse transmitted by the cushioning to product needs to liebelow 119878

119888

From then on many researchers worked on the theo-retical analysis of the shock response of different linear ornonlinear cushioning packaging systems with various shockpulses [5ndash10] and the conducting study was graduated indepth fromone-degree to three-degree systems [11ndash13] Shockresponse spectrum is now wildly used in experimental testsconsidering not only shock condition but also vibration [1415]

Inmany cases damage of products happened along struc-tural elements and damage of structural elements caused thefailure of products Suhir theoretically analyzed the shock andvibration responses of circuit boards of portable electronicproducts and found that the maximum dynamic stress isthe key factor which caused the failure of the product [16]The research on the packaging system of impeller washingmachine gave a similar conclusion

2 The Packaging System ofthe Washing Machine

An impeller washing machine is composed of a washingtank a suspension system and an outer tankThe suspensionsystem is made up of four suspenders which suspend thewashing tank inside the outer tank which decreases trans-mitted vibrations from working washing tank During thedelivery the washing machine is packed with a top cushionpad a bottom cushion pad and four corner holders (seeFigure 2) At the center of the bottom cushion pad there is araised bulge which can uplift the washing tank to release thesuspension

The cushion packaging (the cushion material thick ofcrash pad and so on) of washingmachinewas designed basedon damaged boundary Figure 3 shows the designed cushionmats

In this research the cushion material was polystyrenefoam The subsequent statistic data show that 20 damages

1998400

1

2

3

2998400

3998400

Figure 2 Cushion packaging of an impeller washing machine 1outer tank 2 suspender 3 washing tank 11015840 top cushion pad 21015840corner holder 31015840 bottom cushion pad

came from a suspension system whose suspenders werestraightenedThe result confused engineers Considering thatthe damage boundary does not include the whole cushionpackage the researcher decided to find out not only thefragility of the washing machine but also the shock responseof the packing system

3 Shock Tests on Unpackaged andPackaged Washing Machine

Test equipment MTS886241 shock test system LansmontTest Partner 3 (TP3) data acquisitions system andDASP dataacquisition system

The shock tests followed ASTM D3332-99 and theschematic diagram of the shock test is shown in Figure 4 [17]During the test the packaging case system of the washingmachine was fastened to the shock table Because the mainprotection is the bottom cushion pad the other cushion padswere ignored in the test Two accelerometers were used onefastened to the shock table and the other at the bottom centerof washing tank to record the input shock pulse and theresponse of washing machine respectively The two differentdata acquisition systems have their own accelerometers andthey were in pairs fixed very close to make sure each pairinggets almost the same signal

To confirm that the two data acquisition systems couldgive same recordings a field test was set up and the acquiredsignals from two channels were shown in Figure 5 In thetests half-sine shock pulse was provided by a wave generatorprovided

As shown in Figure 5 the maximum acquired accelera-tions were 908023ms2 (from DASP) and 90287ms2 (fromTP3) respectivelyThedifference of two systems is 06 Bothintervals of two peak accelerations from two different systemsare 01 sTherefore the records from the two systems aremuchclose to each other


(a) (b)

(c)


Fence

Outer tank

Suspender


Shock table

Drop height

Wave generator

Acceleration sensor

Input 1





000 002 004 006 008 010 012

05

04

03

02

01

00

minus01

minus02

minus03

minus04

minus05

times104

Time (s)

Acce

lera

tion

(ms

2 )

(a) DASP

1000

Acce

lera

tion

(ms

2 )

0

Time (ms)

120010008006004002000


(b) TP3



Figure 6 Suspender






Drop height(mm)



50 908 24070 1143 292100 1382 500120 1523 1274150 (failure) 1716 1501






Acce

lera

tion

(ms

2 )

Time (s)

500

400

300

200

100

0

minus100

minus200

minus300

minus400

minus500000 002 004 006 008 010 012



Drop height(mm)



150 1752 253250 1904 295350 2213 369400 (failure) 2441 448





0

20

40

60

80

100

120

140

0 5000 10000 15000 20000 25000

Acce

lera

tion

(ms

2 )

Fn (Hz)














+ + +x

yz

xy

z

y

z


Strain ()

Stre

ss (M

Pa)

05

04

03

02

01

00

0 10 20 30 40 50 60 70 80




AA

AA

A

B

BB B B

25

20

15

10

5

0

minus5

minus10

LS-DYNA user input

0 1 2 3 4 5


B4379A4632

Z-a

ccel

erat

ion

(E+3

) (m

ms

2 )




5 Conclusion



A

AA

A A

Element number12055

10

5

0

minus5

minus10

minus15

minus200 1 2 3 4 5


Axi

al fo

rce (

E+3

) (N

)

A

LS-DYNA user input




360 355350 308340 290






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c)


Fence

Outer tank

Suspender


Shock table

Drop height

Wave generator

Acceleration sensor

Input 1





000 002 004 006 008 010 012

05

04

03

02

01

00

minus01

minus02

minus03

minus04

minus05

times104

Time (s)

Acce

lera

tion

(ms

2 )

(a) DASP

1000

Acce

lera

tion

(ms

2 )

0

Time (ms)

120010008006004002000


(b) TP3



Figure 6 Suspender






Drop height(mm)



50 908 24070 1143 292100 1382 500120 1523 1274150 (failure) 1716 1501






Acce

lera

tion

(ms

2 )

Time (s)

500

400

300

200

100

0

minus100

minus200

minus300

minus400

minus500000 002 004 006 008 010 012



Drop height(mm)



150 1752 253250 1904 295350 2213 369400 (failure) 2441 448





0

20

40

60

80

100

120

140

0 5000 10000 15000 20000 25000

Acce

lera

tion

(ms

2 )

Fn (Hz)














+ + +x

yz

xy

z

y

z


Strain ()

Stre

ss (M

Pa)

05

04

03

02

01

00

0 10 20 30 40 50 60 70 80




AA

AA

A

B

BB B B

25

20

15

10

5

0

minus5

minus10

LS-DYNA user input

0 1 2 3 4 5


B4379A4632

Z-a

ccel

erat

ion

(E+3

) (m

ms

2 )




5 Conclusion



A

AA

A A

Element number12055

10

5

0

minus5

minus10

minus15

minus200 1 2 3 4 5


Axi

al fo

rce (

E+3

) (N

)

A

LS-DYNA user input




360 355350 308340 290






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










000 002 004 006 008 010 012

05

04

03

02

01

00

minus01

minus02

minus03

minus04

minus05

times104

Time (s)

Acce

lera

tion

(ms

2 )

(a) DASP

1000

Acce

lera

tion

(ms

2 )

0

Time (ms)

120010008006004002000


(b) TP3



Figure 6 Suspender






Drop height(mm)



50 908 24070 1143 292100 1382 500120 1523 1274150 (failure) 1716 1501






Acce

lera

tion

(ms

2 )

Time (s)

500

400

300

200

100

0

minus100

minus200

minus300

minus400

minus500000 002 004 006 008 010 012



Drop height(mm)



150 1752 253250 1904 295350 2213 369400 (failure) 2441 448





0

20

40

60

80

100

120

140

0 5000 10000 15000 20000 25000

Acce

lera

tion

(ms

2 )

Fn (Hz)














+ + +x

yz

xy

z

y

z


Strain ()

Stre

ss (M

Pa)

05

04

03

02

01

00

0 10 20 30 40 50 60 70 80




AA

AA

A

B

BB B B

25

20

15

10

5

0

minus5

minus10

LS-DYNA user input

0 1 2 3 4 5


B4379A4632

Z-a

ccel

erat

ion

(E+3

) (m

ms

2 )




5 Conclusion



A

AA

A A

Element number12055

10

5

0

minus5

minus10

minus15

minus200 1 2 3 4 5


Axi

al fo

rce (

E+3

) (N

)

A

LS-DYNA user input




360 355350 308340 290






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Acce

lera

tion

(ms

2 )

Time (s)

500

400

300

200

100

0

minus100

minus200

minus300

minus400

minus500000 002 004 006 008 010 012



Drop height(mm)



150 1752 253250 1904 295350 2213 369400 (failure) 2441 448





0

20

40

60

80

100

120

140

0 5000 10000 15000 20000 25000

Acce

lera

tion

(ms

2 )

Fn (Hz)














+ + +x

yz

xy

z

y

z


Strain ()

Stre

ss (M

Pa)

05

04

03

02

01

00

0 10 20 30 40 50 60 70 80




AA

AA

A

B

BB B B

25

20

15

10

5

0

minus5

minus10

LS-DYNA user input

0 1 2 3 4 5


B4379A4632

Z-a

ccel

erat

ion

(E+3

) (m

ms

2 )




5 Conclusion



A

AA

A A

Element number12055

10

5

0

minus5

minus10

minus15

minus200 1 2 3 4 5


Axi

al fo

rce (

E+3

) (N

)

A

LS-DYNA user input




360 355350 308340 290






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













+ + +x

yz

xy

z

y

z


Strain ()

Stre

ss (M

Pa)

05

04

03

02

01

00

0 10 20 30 40 50 60 70 80




AA

AA

A

B

BB B B

25

20

15

10

5

0

minus5

minus10

LS-DYNA user input

0 1 2 3 4 5


B4379A4632

Z-a

ccel

erat

ion

(E+3

) (m

ms

2 )




5 Conclusion



A

AA

A A

Element number12055

10

5

0

minus5

minus10

minus15

minus200 1 2 3 4 5


Axi

al fo

rce (

E+3

) (N

)

A

LS-DYNA user input




360 355350 308340 290






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










A

AA

A A

Element number12055

10

5

0

minus5

minus10

minus15

minus200 1 2 3 4 5


Axi

al fo

rce (

E+3

) (N

)

A

LS-DYNA user input




360 355350 308340 290






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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